Find the area between the graphs of.....(calc 2 question)

Question

Find the area between the graphs of ƒ(x)=cos(x) and g(x)= sin(2x) over the interval [-pi/2, pi/2]. Recall, the area between two curves on the interval [a,b] is ∫_a^b | ƒ(x)-g(x) | dx. It is a very good idea to sketch a graph of this situation to help you understand how to proceed.

Sorry I cannot find the pi symbol for the life of me and the integral sign doesn't seem to come with a place to input your (a, b) variables so I worked with what I could!

Answer 1

Annie,

1) I agree that it would be great to see a picture of your work--easy to get the "right" answer the wrong way

2) 2 is the correct value, and you might want to say what you found for the anti-derivatives

3) Odd functions have "double-flip" symmetry--flip the graph over the x-axis, then flip that over the y-axis--- (f(-x) = -1*f(x)) so there is the same amount of area below the x-axis as above, and definite integrals are "signed" area, so you get a value of zero when you have limits of integration which are opposite values

Hope this helps--Andrew F.